Jonathan M. Henshaw

Statistical associations between two variables can arise via various causal mechanisms. For example, one variable may influence the other, or they may share common causes. Surprisingly little attention has been devoted to quantifying how such causal pathways contribute to the overall association between variables. Here, I present two methods for partitioning a covariance between variables X and Z into a causal component arising from the effect of X and Z and a spurious component arising via other pathways. Both methods rely on averaging causal decompositions over the distributions of the variables, but the decomposition and averaging are performed in different ways. The ‘gradient’ definition decomposes causal effects in the neighbourhood of naturally occurring values, making it relatively straightforward to estimate. It assumes that the cause variable X is normally distributed. In contrast, the ‘two-step’ definition decomposes large (‘step-wise’) changes in values and makes no distributional assumptions. I describe applications of these methods to analysing natural selection and illustrate them using the covariance between body size and the number of eggs carried by pregnant male dusky pipefish, Syngnathus floridae . I partition this total covariance into a causal component due to the effect of body size on egg number and a spurious component arising from variation in body size and egg number among collection sites.

Male and female animals often differ remarkably in their reproductive behaviours, typified by competing males and caring females. One influential explanation traces sex-role divergence to anisogamy: sex differences in gamete size. This explanation remains controversial, because existing models have not fully resolved how anisogamy leads to secondary sex-role divergence, and exceptions to typical patterns are empirically well-documented. Here, we develop mathematical models linking anisogamy to secondary sex-role evolution, showing that anisogamy drives sex-role divergence along contrasting evolutionary trajectories depending on ecological context. When the sexes differ only in gamete size, male-biased mating competition and offspring care evolve under ‘scramble competition’, whereas uncertain paternity shifts the population towards typical patterns. By contrast, anisogamy generally drives typical sex roles under ‘contest competition’, although sex-role reversal can emerge as an alternative stable state when care must be apportioned among offspring. Anisogamy can thus explain the striking diversity of sex differences across taxa.

We investigate the evolutionary dynamics of sexually selected traits using both a mathematical model and comparative analyses, focusing on the relative rates of evolution between male ornaments and weapons. In our framework, ornaments evolve jointly with female preferences, whereas weapons evolve under direct male–male competition. Our theoretical model predicts that coevolution with mate preference is the key driver of the accelerated evolution of ornaments. Stochastic drift in female preferences causes fluctuating selection on male ornaments, resulting in rapid evolutionary change in ornament size. In contrast, weapons evolve more slowly due to the more stable selection generated by male–male competition. In the empirical part of the study, we used Brownian motion and Ornstein–Uhlenbeck models to measure the rate of trait evolution across various taxa and found that ornaments generally evolve at faster rates than weapons, consistent with the predictions of our theoretical modelling. Together, these results demonstrate how preference-driven dynamics can accelerate ornament evolution, revealing a key asymmetry between the inter- and intrasexual mechanisms of sexual selection. Our findings contribute to a deeper understanding of how different forms of sexual selection shape trait evolution on macroevolutionary timescales.

Phenotypic traits rarely evolve in isolation. Instead, multiple traits typically interact to influence fitness, resulting in complex coevolutionary dynamics. Such dynamics can be predicted using mathematical frameworks, such as adaptive dynamics and quantitative genetics. Selection gradients play a crucial role in these frameworks, describing the direction and strength of selection and thus predicting evolutionary trajectories and potential endpoints. Current theory focuses mainly on analysing how traits change in response to selection, which changes over time as traits evolve. However, the extent to which changes in each trait contribute to changes in the selection environment remains unquantified, leaving much of our understanding of trait coevolution reliant on verbal reasoning. To advance a more comprehensive and quantitative understanding of coevolutionary dynamics, we develop a general framework that examines how trait changes feedback to influence the selection environment. This framework enables a fine-grained and systematic investigation of coevolutionary feedback between traits and selection gradients by quantifying the pathways through which they influence one another. Our framework can be applied both to adaptive-dynamic models and to quantitative-genetic models under the weak selection limit. We illustrate our approach with three examples that showcase its potential to deepen our understanding of established models.

Evolutionary trade-offs—opposing trait effects on total fitness via different fitness components—are likely to be widespread. Some key trade-offs are expected to be the result of chains of causation acting across an organism’s lifetime. For example, a trait imparting reproductive benefits early in life may trade off against reduced survival to attain later-life reproductive opportunities. Tools in evolutionary quantitative genetics have recently been developed to formally characterize selection acting through different causal pathways throughout the life cycle and, therefore, to formally characterize evolutionary trade-offs. We use these methods to investigate a trade-off between early life reproduction and survival and how that trade-off affects selection on body size in the Soay sheep population inhabiting St Kilda (Outer Hebrides, Scotland). We decompose and quantify the total effects of first-year female body mass on lifetime fitness, with particular attention to the effect of body mass on early-life reproduction and the potential survival cost of early-life reproduction. Our results establish that the total effect of body mass on lifetime fitness is positive, despite the strong negative contribution acting via early life reproduction. Moreover, we show that the magnitude of the selection on body mass acting through different causal paths highly depends on population density. At higher densities, the cost of early-life reproduction is higher, and therefore, it contributes a strong negative component to the total selection of body mass—i.e., at higher population density, selection on body mass is weaker than it is when the population density is smaller. By decomposing total selection and quantifying selection acting through different causal paths, we expose the underlying mechanics shaping body mass in Soay sheep female lambs, and we provide a meaningful contribution to the understanding of the evolution of body size in this population.

The Bateman gradient is a fundamental metric of sexual selection, often interpreted as the fitness advantage individuals gain by increasing their number of mates. However, it is recognized that any traits influencing both mating and reproductive success can confound the gradient, misrepresenting the strength of precopulatory sexual selection. Yet, the magnitude of this misrepresentation across different biological systems (e.g., differing in anisogamy or strength of sperm competition), which covariates are most problematic, or how confounded relationships can be diagnosed to better interpret the Bateman gradient, remains largely unexplored. To address these gaps, we simulate 9 plausible biological scenarios where the effect of male mating success on reproductive success is confounded. We find that covariances between male mating success and female fecundity or egg allocation confound male Bateman gradients more strongly than covariances between male mating success and ejaculate traits. These differences in the impact of male–female vs. male–male covariances are especially pronounced in systems with high levels of anisogamy and no sperm competition. We provide guidelines for empiricists to visually identify such covariances by recording mating order, and suggest that researchers explicitly state causal assumptions when interpreting Bateman gradients. Additionally, when the covariate is a confounder, not a mediator, we demonstrate that partial Bateman gradients allow better interpretation of the strength of precopulatory sexual selection. These insights into the mechanisms driving variation in the Bateman gradient allow us to clarify its meaning, identify scenarios where its interpretation might be problematic, and offer practical solutions to address this.

Artificial gene drives offer a promising approach for controlling populations of agricultural pests, invasive species and disease vectors, such as malaria-carrying mosquitoes. Gene-drive alleles induce a transmission bias, meaning there is a greater than 50% probability that they will be inherited by offspring, facilitating their rapid propagation through populations. When these alleles induce high fitness costs, their spread can lead to the eradication of target populations. While gene drives hold great potential, there are various barriers that can hinder their effectiveness. One such barrier, precopulatory mate choice, has been suggested to impact the spread of gene drives, yet it remains underexplored. Here, we use individual-based simulations to investigate the spread of gene drives while allowing female mating preferences to evolve. In our model, gene-drive alleles exhibit transmission bias but also incur survival costs. Crucially, females are assumed to be able to distinguish between drive carriers and wild-type males based on drive-associated phenotypic differences. Consequently, females can evolve to prefer wild- type or drive-carrying males as mates. Our simulations show that under certain parameter settings, mating preferences against drive carriers can evolve during the spread of a gene drive. This can result in the eradication of the drive alleles and the evolutionary rescue of the population. The impact of mate choice was most pronounced when the gene drive spread relatively slowly, as this allowed more time for preferences against drives to evolve. In addition, evolutionary rescue occurred less frequently for recessive drives than for dominant ones. Our results demonstrate that mate choice can indeed impair the effectives of gene drive as a mechanism of population control and should therefore be seen as a potential risk. We further consider the implications for scientists developing gene drives as a population control technology. Lay summary: Most genes exist in multiple versions called alleles, with each having a 50% chance of being passed on by parents during sexual reproduction. However, some alleles, known as gene drives, manipulate inheritance to spread more widely across populations, even if they reduce the fitness of individuals carrying them. Gene drives occur naturally but can also be engineered in the laboratory. Recent technological advancements have led scientists to explore gene drives as a promising tool for controlling pests, invasive species, and disease vectors like malaria-carrying mosquitoes. However, before releasing any gene drives into the wild, it is crucial to assess their feasibility and potential risks. Here, we used computer simulations to explore how artificial gene drives spread when mate choice is allowed to evolve, assuming females can differentiate between males carrying gene drives and those without them. While gene drives have a transmission advantage, they also reduce the survival of carriers. Our results show that evolution can act rapidly after a gene drive is released. Females evolve to discriminate against drive-carrying males, which can sometimes result in the eradication of the gene drive. When gene drives have high survival costs, this evolutionary response can prevent population extinction, potentially undermining the drive’s purpose. The impact of mate choice is greatest when gene drives spread slowly, giving more time for evolution to act. These findings highlight the importance of considering mate choice dynamics when developing gene drives for population control.

Phenotypic traits rarely evolve in isolation. Instead, multiple traits typically interact, resulting in complex coevolutionary dynamics. Such dynamics can be predicted using mathematical frameworks such as adaptive dynamics and quantitative genetics. Selection gradients play a crucial role in these frameworks, describing the direction and strength of selection and predicting evolutionary trajectories and potential endpoints. Current theory focuses mainly on analysing how traits change in response to selection. However, selection gradients also change over time as traits evolve. For a complete understanding of coevolutionary dynamics, it is consequently essential to examine how trait changes feed back to influence the selection environment. Here, we develop a general framework for investigating coevolutionary feedback between traits and selection gradients. Rather than relying on verbal interpretation of causal relationships, our approach explicitly quantifies the various pathways by which traits and selection gradients influence one another. Our framework can be applied both to adaptive-dynamic models and to quantitative-genetic models under the weak selection limit. We illustrate our approach with three examples that showcase its potential to deepen our understanding of established models.

The Bateman gradient (BG or 𝛽 _???????? ) is a fundamental metric of sexual selection, and is often interpreted as the fitness advantage individuals can gain by increasing their number of mates. However, researchers commonly misconceive the relationship between mating success (MS) and reproductive success (RS) as always being causal, leading to a misinterpretation of the BG. The BG is phenomenological and therefore uninformative about the mechanisms leading to correlations between MS and RS. Here, we simulate sequential matings in males from biological systems with varying levels of anisogamy and sperm competition, to better understand the underlying processes that modulate male BGs. We show that the BG does not solely reflect the causal influence of MS on RS as is typically interpreted, but is also a consequence of covariances between male MS and male ejaculate traits, female fecundity, or female post-mating decisions. For example, we show that the BG is substantially shallower when the ejaculate size of males negatively co-varies with their MS, such as in species with alternative male reproductive tactics. Such covariances can lead to a misinterpretation of the measured BG, because here, it does not merely represent the strength of selection on intra-sexual competition for mates. We suggest how such covariances can be visually assessed, and accounted for using partial Bateman gradients, to better interpret the influence of MS on RS, thus the strength of pre-copulatory sexual selection. Among other simplifications, our simulations have a male-only focus, but they provide insights into the mechanisms driving inter- and intra-specific variation in the BG, clarify its meaning, and improve our understand of sexual selection.